New photon-counting formula in thermo field dynamics

Abstract

We show that the probability distribution $p\left(m,T\right)$ of registering m photoelectrons can be explained in Thermo Field Dynamics theory as a matrix element of thermo entangling operator $e^{\left(1-\mathit{\xi }\right)a^{†}{\tilde{a}}^{†}}$ between $\left.〈\mathit{\rho }\right|={\sum }_m\left.〈m,\tilde{m}\right|\mathit{\rho }$ and $\left|m,\tilde{m}\right.〉=\left|m\right.〉\left|\tilde{m}\right.〉$ where $\left|\tilde{m}\right.〉$ is a fictitious Fock state. Based on this, the new integration formula for calculating $p\left(m,T\right),$ which involves both Laguerre polynomial and the characteristic function $\mathit{\chi }\left(\mathit{\eta }\right)$ of ρ, is obtained. This provides us with convenience for evaluating photoelectric counting probability for various optical fields.

Keywords:

• Photon-counting
• thermo entangled state
• IWOP method
• entangled state representation